We construct families of incoherent matter-wave solitons in a repulsive degenerate Bose gas trapped in an optical lattice (OL), i.e., gap solitons, and investigate their stability at zero and finite temperature, using the Hartree-Fock-Bogoliubov equations. The gap solitons are composed of a coherent condensate, and normal and anomalous densities of incoherent vapor cotrapped with the condensate. Both intragap and intergap solitons are constructed, with chemical potentials of the components falling in one or different band gaps in the OL-induced spectrum. Solitons change gradually with temperature. Families of intragap solitons are completely stable (both in direct simulations and in terms of eigenvalues of perturbation modes), while the intergap family may have a very small unstable eigenvalue (nevertheless, they feature no instability in direct simulations). Stable higher-order (multihumped) solitons and bound complexes of fundamental solitons are found too.

We investigate quantum and temperature fluctuations of a vortex lattice in a one-dimensional optical lattice. We discuss in particular the Bloch bands of the Tkachenko modes and calculate the correlation function of the vortex positions along the direction of the optical lattice. Because of the small number of particles in the pancake Bose-Einstein condensates at every site of the optical lattice, finite-size effects become very important. Moreover, the fluctuations in the vortex positions are inhomogeneous due to the inhomogeneous density. As a result, the melting of the lattice occurs from the outside inwards. However, tunneling between neighboring pancakes substantially reduces the inhomogeneity as well as the size of the fluctuations. On the other hand, nonzero temperatures increase the size of the fluctuations dramatically. We calculate the crossover temperature from quantum melting to classical melting. We also investigate melting in the presence of a quartic radial potential, where a liquid can form in the center instead of at the outer edge of the pancake Bose-Einstein condensates.

We investigate stability of gap solitons (GSs) in the first two band gaps in the framework of the one-dimensional Gross-Pitaevskii equation, combining the repulsive nonlinearity and a moderately strong optical lattice (OL), which is subjected to “management,” in the form of time-periodic modulation of its depth. The analysis is performed for parameters relevant to the experiment, characteristic values of the modulation frequency being $\omega \sim 2\pi \times 20\mathrm{Hz}$. First, we present several GS species in the two band gaps in the absence of the management. These include fundamental solitons and their bound states, as well as a subfundamental soliton in the second gap, featuring two peaks of opposite signs in a single well of the periodic potential. This soliton is always unstable, and quickly transforms into a fundamental GS, losing a considerable part of its norm. In the first band gap, (stable) bound states of two fundamental GSs are possible solely with opposite signs, if they are separated by an empty site. Under the periodic modulation of the OL depth, we identify stability regions for various GS species, in terms of $\omega$ and modulation amplitude, at fixed values of the soliton’s norm, $N$. In either band gap, the GS species with smallest $N$ has a largest stability area; in the first and second gaps, they are, respectively, the fundamental GS proper, or the one spontaneously generated from the subfundamental soliton. However, with the increase of $N$, the stability region of every species expands in the first gap, and shrinks in the second one. The outcome of the instability development is also different in the two band gaps: it is destruction of the GS in the first gap, and generation of extra side lobes by unstable GSs in the second one.

We investigate the features of the spontaneous emission spectra in a coherently driven cold five-level atomic system by means of a radio frequency (rf) or microwave field driving a hyperfine transition within the ground state. It is shown that a few interesting phenomena such as spectral-line narrowing, spectral-line enhancement, spectral-line suppression, and spontaneous emission quenching can be realized by modulating the frequency and intensity of the rf-driving field in our system. In the dressed-state picture of the coupling and rf-driving fields, we find that this coherently driven atomic system has three close-lying levels so that multiple spontaneously generated coherence (SGC) arises. Our considered atomic model can be found in real atoms, such as rubidium or sodium, so a corresponding experiment can be done to observe the expected phenomena related to SGC reported by Fountoulakis et al. [Phys. Rev. A 73, 033811 (2006)], since no rigorous conditions are required.

We propose an optical lattice for cold atoms made of a one-dimensional stack of dark ring traps. It is obtained through the interference pattern of a standard Gaussian beam with a counterpropagating hollow beam obtained using a setup with two conical lenses. The traps of the resulting lattice are characterized by a high confinement and a filling rate much larger than unity, even if loaded with cold atoms from a magneto-optical trap. We have implemented this system experimentally, and demonstrated its feasibility. Applications in statistical physics, quantum computing, and Bose-Einstein condensate dynamics are conceivable.

We analyze the entanglement between two modes of a free Dirac field as seen by two relatively accelerated parties. The entanglement is degraded by the Unruh effect and asymptotically reaches a nonvanishing minimum value in the infinite acceleration limit. This means that the state always remains entangled to a degree and can be used in quantum information tasks, such as teleportation, between parties in relative uniform acceleration. We analyze our results from the point of view afforded by the phenomenon of entanglement sharing and in terms of recent results in the area of multiqubit complementarity.

We investigate the state space of bipartite qutrits. For states which are locally maximally mixed we obtain an analog of the “magic” tetrahedron for bipartite qubits—a magic simplex $\mathcal{W}$. This is obtained via the Weyl group which is a kind of “quantization” of classical phase space. We analyze how this simplex $\mathcal{W}$ is embedded in the whole state space of two qutrits and discuss symmetries and equivalences inside the simplex $\mathcal{W}$. Because we are explicitly able to construct optimal entanglement witnesses we obtain the border between separable and entangled states. With our method we find also the total area of bound entangled states of the parameter subspace under intervestigation. Our considerations can also be applied to higher dimensions.

The atom fluctuation statistics of an ideal, mesoscopic, Bose-Einstein condensate are investigated from several different perspectives. By generalizing the grand canonical analysis (applied to the canonical ensemble problem), we obtain a self-consistent equation for the mean condensate particle number that coincides with the microscopic result calculated from the laser master equation approach. For the case of a harmonic trap, we obtain an analytic expression for the condensate particle number that is very accurate at all temperatures, when compared with numerical canonical ensemble results. Applying a similar generalized grand canonical treatment to the variance, we obtain an accurate result only below the critical temperature. Analytic results are found for all higher moments of the fluctuation distribution by employing the stochastic path integral formalism, with excellent accuracy. We further discuss a hybrid treatment, which combines the master equation and stochastic path integral analysis with results obtained based on the canonical ensemble quasiparticle formalism [Kocharovsky et al., Phys. Rev. A 61, 053606 (2000)], producing essentially perfect agreement with numerical simulation at all temperatures.

It is predicted that the near-threshold nondipole photoelectron angular distribution parameters of valence $ns$ electrons from atoms having an $n{d}^5$ half-filled shell in the ground state differ markedly for different final-state terms of the residual ion. This is due to the strong term dependence of electron correlation in these systems. As an example, the nondipole $4s$-photoelectron angular distribution parameters below the $3d$ ionization threshold of the $\mathrm{Mn}\left(3d^{5}4s^2{}^{6}S\right)$ atom, leading to ${\mathrm{Mn}}^{+}\left(4s^1{}^{7}S\right)$ and ${\mathrm{Mn}}^{+}\left(4s^1{}^{5}S\right)$, have been calculated within the framework of the “spin-polarized” random phase approximation with exchange. The phenomenon should be a general property of all half-filled shell atoms and ions.

Together with the Zhu-Nakamura nonadiabatic transition formulas to treat the coupled electronic and nuclear quantum tunneling probability, we generalize quantum Kramers theory to electron-transfer rate constants. The application in the strongly condensed phase manifests that the approach correctly bridges the gap between the nonadiabatic (Fermi golden rule) and adiabatic (Kramers theory) limits in a unified way, and leads to good agreement with the quantum path integral data at low temperature.

A theoretical description of the dissociative recombination process for the ${\mathrm{HCO}}^{+}$ ion suggests that the nonadiabatic Renner-Teller coupling between electronic and vibrational degrees of freedom plays an important role. This finding is consistent with a recent study of this process for another closed-shell molecule, the ${{\mathrm{H}}_3}^{+}$ ion, where Jahn-Teller coupling was shown to generate a relatively high rate. The cross section obtained here for the dissociative recombination of ${\mathrm{HCO}}^{+}$ exhibits encouraging agreement with a merged-beam experiment.

The possibility of achieving highly selective excitation of low metastable states of hydrogen and helium atoms by using short laser pulses with reasonable parameters is demonstrated theoretically. Interactions of atoms with the laser field are studied by solving the close-coupling equations without discretization. The parameters of laser pulses are calculated using different kinds of optimization procedures. For the excitation durations of hundreds of femtoseconds direct optimization of the parameters of one and two laser pulses with Gaussian envelopes is used to introduce a number of simple schemes of selective excitation. To treat the case of shorter excitation durations, optimal control theory is used and the calculated optimal fields are approximated by sequences of pulses with reasonable shapes. A way to achieve selective excitation of metastable atomic states by using sequences of attosecond pulses is introduced.

We present the theory of bosonic systems with multiple condensates, providing a unified description of various model systems that are found in the literature. We discuss how degeneracies, interactions, and symmetries conspire to give rise to this unusual behavior. We show that as degeneracies multiply, so do the varieties of fragmentation, eventually leading to strongly correlated states with no trace of condensation.

We consider dynamical stabilization of Bose-Einstein condensates by time-dependent modulation of the scattering length. The problem has been studied before by several methods: Gaussian variational approximation, the method of moments, the method of modulated Townes soliton, and the direct averaging of the Gross-Pitaevskii equation. We summarize these methods and find that the numerically obtained stabilized solution has a different configuration than that assumed by the theoretical methods (in particular a phase of the wave function is not quadratic with $r$). We show that there is presently no clear evidence for stabilization in a strict sense, because in the numerical experiments only metastable (slowly decaying) solutions have been obtained. In other words, neither numerical nor mathematical evidence for a new kind of soliton solutions has been revealed so far. The existence of the metastable solutions is nevertheless an interesting and complicated phenomenon on its own. We try some non-Gaussian variational trial functions to obtain better predictions for the critical nonlinearity $g_{cr}$ for metastabilization but other dynamical properties of the solutions remain difficult to predict.

A dynamical theory is developed with the purpose of explaining recent experimental results on multiphoton-excited amplified stimulated emission (ASE). Several conspicuous features of this experiment are analyzed, like the threshold dependence of the spectral profile on the pump intensity, and spectral shifts of the ASE pulses co- and counterpropagating relative to the pump pulse. Two models are proposed and evaluated, one based on the isolated molecule and another which involves solvent interaction. The spectral shift between the forward and backward ASE pulses arises in the first model through the competition between the ASE transitions from the pumped vibrational levels and from the bottom of the excited-state well, while in the solvent-related model the dynamical solute-solvent interaction leads to a relaxed excited state, producing an additional ASE channel. In the latter model the additional redshifted ASE channel makes the dynamics of ASE essentially different from that in the molecular model because the formation of the relaxed state takes a longer time. The variation of the pump intensity influences strongly the relative intensities of the different ASE channels and, hence, the spectral shape of ASE in both models. The regime of ASE changes character when the pump intensity crosses a threshold value. Such a phase transition occurs when the ASE rate approaches the rate of vibrational relaxation or the rate of solute-solvent relaxation in the first excited state.

We show that a divergence in the optical polarizability of a heterogeneous medium with nonlinear amplification and a strong dipole-dipole interaction between particles can lead to a phase transition, for which the dipole momentum of the particles or the dipole radiation rate can be taken as order parameters. The “dipole laser” [Phys. Rev. A 71, 063812 (2005)] can be used both as a simple example of such a second-order phase transition and to provide a recipe for its analysis. We show that similar phase transitions may be possible for a nanoparticle on the surface of an optically active medium and at the “Clausius-Mossotti” catastrophe in a bulk heterogeneous medium.

Absolute angle-differential cross sections for electron-impact excitation of argon and xenon atoms to the lowest four $n{p}^5(n+1)s$ levels, and the $5p^{5}5d[7∕2{]}_3$ level in xenon, have been measured and calculated as a function of electron energy up to a few eV above threshold at a fixed scattering angle of $135°$. For argon, very good agreement is observed between the experimental data and predictions from a Breit-Pauli $B$-spline $R$-matrix (BSR) method, in which nonorthogonal orbital sets are used to optimize the target description. The agreement is still satisfactory for the more complex xenon target, suggesting that predictions from the BSR model should already be sufficiently accurate for many modeling applications. Nevertheless, the remaining discrepancies indicate the need for further refinement of the theoretical model.

We investigate the thermodynamic properties of a Bose-Einstein condensate with negative scattering length confined in a toroidal trapping potential. By numerically solving the coupled Gross-Pitaevskii and Bogoliubov–de Gennes equations, we study the phase transition from the uniform state to the symmetry-breaking state characterized by a bright-soliton condensate and a localized thermal cloud. In the localized regime, three states with a finite condensate fraction are present: the thermodynamically stable localized state, a metastable localized state, and also a metastable uniform state. Remarkably, the presence of the stable localized state strongly increases the critical temperature of Bose-Einstein condensation.

We present a method for multipartite entanglement purification of any stabilizer state shared by several parties. In our protocol each party measures the stabilizer operators of a quantum error-correcting code on his or her qubits. The parties exchange their measurement results, detect or correct errors, and decode the desired purified state. We give sufficient conditions on the stabilizer codes that may be used in this procedure and find that Steane’s seven-qubit code is the smallest error-correcting code sufficient to purify any stabilizer state. An error-detecting code that encodes two qubits in six can also be used to purify any stabilizer state. We further specify which classes of stabilizer codes can purify which classes of stabilizer states.